Each game on Steam has a unique identifier and this is mapped to a specific item in our database. The item in our database has a SKU (Stock Keeping Unit) that identifies what version of the game you own (for example Stellaris has three different SKUs, one for each edition). This SKU is then mapped towards the Owned Item part of the forum and grants access and/or icons.
We can't see your CD key for example nor can we see any specific details of your copy other than which version. The only exception to this is if it's bought from Paradox Plaza, then we see the CD key as well as transaction ID (as they are needed for support matters).